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A posteriori estimators for the h-p version of the finite element method in 1D

Authors:

Alfred Schmidt,

Kunibert G. SiebertAuthors Info & Claims

Applied Numerical Mathematics, Volume 35, Issue 1

Pages 43 - 66

https://doi.org/10.1016/S0168-9274(99)00046-X

Published: 01 September 2000 Publication History

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Ferguson ZSchneider TKaufman DPanozzo D(2023)In-Timestep Remeshing for Contacting ElastodynamicsACM Transactions on Graphics10.1145/359242842:4(1-15)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592428
Koschier DDeul CBrand MBender J(2017)An $hp$-Adaptive Discretization Algorithm for Signed Distance Field GenerationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2017.273020223:10(2208-2221)Online publication date: 31-Aug-2017
https://dl.acm.org/doi/10.1109/TVCG.2017.2730202
Canuto CNochetto RStevenson RVerani M(2017)Convergence and optimality of $${\mathbf {hp}}$$hp-AFEMNumerische Mathematik10.1007/s00211-016-0826-x135:4(1073-1119)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1007/s00211-016-0826-x
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Index Terms

A posteriori estimators for the h-p version of the finite element method in 1D
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations in finite fields

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 September 2000

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Ferguson ZSchneider TKaufman DPanozzo D(2023)In-Timestep Remeshing for Contacting ElastodynamicsACM Transactions on Graphics10.1145/359242842:4(1-15)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592428
Koschier DDeul CBrand MBender J(2017)An $hp$-Adaptive Discretization Algorithm for Signed Distance Field GenerationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2017.273020223:10(2208-2221)Online publication date: 31-Aug-2017
https://dl.acm.org/doi/10.1109/TVCG.2017.2730202
Canuto CNochetto RStevenson RVerani M(2017)Convergence and optimality of $${\mathbf {hp}}$$hp-AFEMNumerische Mathematik10.1007/s00211-016-0826-x135:4(1073-1119)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1007/s00211-016-0826-x
Canuto CSimoncini VVerani M(2015)Contraction and Optimality Properties of an Adaptive Legendre---Galerkin MethodJournal of Scientific Computing10.1007/s10915-014-9912-363:3(769-798)Online publication date: 1-Jun-2015
https://dl.acm.org/doi/10.1007/s10915-014-9912-3
Mitchell WMcClain M(2014)A Comparison of hp-Adaptive Strategies for Elliptic Partial Differential EquationsACM Transactions on Mathematical Software10.1145/262945941:1(1-39)Online publication date: 27-Oct-2014
https://dl.acm.org/doi/10.1145/2629459
Canuto CNochetto RVerani M(2014)Contraction and optimality properties of adaptive Legendre-Galerkin methodsComputers & Mathematics with Applications10.1016/j.camwa.2013.05.02567:4(752-770)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1016/j.camwa.2013.05.025
Bank RParsania ASauter S(2013)Saturation estimates for hp-finite element methodsComputing and Visualization in Science10.1007/s00791-015-0234-216:5(195-217)Online publication date: 1-Oct-2013
https://dl.acm.org/doi/10.1007/s00791-015-0234-2
Bank RNguyen H(2011)hp Adaptive finite elements based on derivative recovery and superconvergenceComputing and Visualization in Science10.1007/s00791-012-0179-714:6(287-299)Online publication date: 1-Aug-2011
https://dl.acm.org/doi/10.1007/s00791-012-0179-7
Dörfler WHeuveline V(2007)Convergence of an adaptive hp finite element strategy in one space dimensionApplied Numerical Mathematics10.1016/j.apnum.2006.10.00357:10(1108-1124)Online publication date: 1-Oct-2007
https://dl.acm.org/doi/10.1016/j.apnum.2006.10.003
Demkowicz LRachowicz WDevloo P(2002)A Fully Automatic hp-AdaptivityJournal of Scientific Computing10.1023/A:101519231270517:1-4(117-142)Online publication date: 1-Dec-2002
https://dl.acm.org/doi/10.1023/A%3A1015192312705

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The $P_1^\protect\lowercasemod$ Element: A New Nonconforming Finite Element for Convection-Diffusion Problems

Superconvergence of the h-p version of the finite element method in one dimension

Hierarchical A Posteriori Error Estimators for Mortar Finite Element Methods with Lagrange Multipliers

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